kosinimuunnokseen

Kosinimuunnos, also known as cosine similarity, is a measure of similarity between two non-zero vectors of an inner product space. It is defined as the cosine of the angle between the vectors, which is a measure of orientation, not magnitude. Cosine similarity is often used in text analysis, information retrieval, and machine learning to compare the similarity between documents, sentences, or other types of data.

The formula for cosine similarity between two vectors A and B is:

cosine_similarity(A, B) = (A · B) / (||A|| ||B||)

where A · B is the dot product of A and B, and ||A|| and ||B|| are the magnitudes (or norms) of A and B, respectively. The dot product measures the extent to which the vectors point in the same direction, while the magnitudes measure the length of the vectors.

Cosine similarity ranges from -1 to 1, where 1 indicates that the vectors are identical, 0 indicates that the vectors are orthogonal (i.e., they have no similarity), and -1 indicates that the vectors are diametrically opposed. In practice, cosine similarity is often used to compare the similarity between documents or sentences, where each document or sentence is represented as a vector of word frequencies or other features.

Cosine similarity is a popular choice for text analysis and information retrieval because it is computationally efficient and can handle high-dimensional data. It is also robust to differences in document length, as it only considers the direction of the vectors, not their magnitude. However, cosine similarity may not be suitable for all types of data, and other similarity measures may be more appropriate in certain contexts.